7.3 Decapitation with the blind spotJearl Walker www.flyingcircusofphysics.comApril 2007 Even if you have full sight, you are blind in a small region of your retina where the optic nerve is connected to the light detectors along the retina. To find this blind spot, fix your gaze on a distant object while you bring a small object across your field of view. Moving a small eraser at arm’s length will do but don’t follow the eraser with your eye; keep your gaze fixed on the distant object. If you bring the eraser to a point about 15º to the temple side of the gaze, the eraser might disappear because its image then falls on the blind spot. You do not normally notice the blind spot because the visual system fills it in, almost as if it does not want you to worry about the lack of image there. By filling in, I mean the visual system completes the scene. For example, if you are looking at a wall, you automatically perceive the wall in the blind spot. Recently, Lothar Spillmann, Tobias Otte, Kai Hamburger (of the University Hospital, Freiburg, Germany), and Sevin Magnussen (of the University of Oslo) found that the filling in of both texture and color depends on the visual scene immediately next to the blind spot (as close as 0.05º from the edge of the blind spot). The visual system apparently samples that adjacent texture and color and then blends it across the blind spot. However, this blending in does not always work, especially if you know enough to “look” for the blind spot. In The Flying Circus of Physics book I describe how one physiological psychologist amused himself by closing one eye and then positioning the blind spot of his open eye on the head of an irritating dinner guest to visually behead the guest. If you are ever bored to tears in a lecture (golly, surely it could not a physics class and surely it could not be my physics class!), you might try positioning the blind spot of one eye on the head of the lecturer.

7.5 Floaters in your eyeJearl Walkerwww.flyingcircusofphysics.comDecember 2014 When I view a bright featureless background such as the clear sky, my field of view is littered with small floating dots and larger structures. The dots each consist of concentric circles, but most of the larger structures are elongated. A large structure in my right eye often interferes with my ability to read with that eye.

Floaters, as they are called, can be seen more clearly if the eye is illuminated by a small source of light. For example, I normally use an illuminated pinhole in opaque cardboard. However, any tiny bright source of light, such as a brightly reflecting paper clip, can also work. (I am very careful about bringing any object close to an eye.)

When I use the pinhole arrangement, I see several other curious features. There are bright specks that seem to lack the concentric circles of the more common floaters. Sometimes I see dark specks and a stationary pattern of dark lines extending from the center of my field of view. Just after I blink, I see bright spots and a pattern of horizontal bright and dark lines. Sometimes I also see stationary bright patches or floating wrinkled patches. Upon opening my eyes in the morning, I might see one or more spots that are much darker or (more rarely) much brighter than the rest of my view.

What causes these various appearances?

The common floaters are probably due to irregularities in the vitreous humor (the transparent material filling most of the eyeball). You cannot see the irregularity itself or even its shadow on the retina. Rather, you see the diffraction pattern the irregularity casts on the retina. Diffraction is a type of interference that light waves undergo when they pass through a small opening or pass by a small obstacle. Here, when light from a pinhole passes an irregularity in the vitreous humor, the light is diffracted into an interference pattern on the retina. The pattern consists of concentric bright bands (where light waves happen to reinforce one another) and dark bands (where they tend to cancel one another).

If the irregularity is roughly circular, the pattern is also, with a bright central spot. An elongated irregularity produces an elongated pattern. The floater you normally see is a blurry diffraction pattern. If you look through a pinhole, you see the pattern more sharply and can distinguish individual bright and dark bands. Floaters drift through your line of sight because the vitreous humor is not rigid and can shift.

Some of the floaters may be due to bits of the vitreous humor that have broken off and that float in the liquid layer in front of the fovea, the pit-like structure where your line of sight falls. They can also be due to blood cells that leak into that liquid layer, but in that case the field of view is likely to be tinted red. Everyone has floaters, and their presence is not necessarily an indication of a medical problem. As you age, you probably will see more floaters.

The bright specks and the pattern of bright and dark lines that follow a blink are due to the liquid (tear) layer left on the cornea. Irregularities in that layer can slightly focus light rays to give the brighter regions. The lines radiating from the center of the view may be from the radial structure of the eye lens. Dark specks may be due to tiny opaque regions in the lens. The dark and bright spots seen by some people just after opening their eyes in the morning are not understood.

x7.8 Eye oscillations, pretzels, and monitor screensJearl Walker www.flyingcircusofphysics.comApril 2007 In The Flying Circus of Physics book, I describe how you can hum in order to “strobe” a television screen. The television image is created line by line and each image line lingers for a short time after it is created. If you hum at the right frequency (and can hold the frequency), the vertical oscillations of the retina allow you to see one or more horizontal black lines on the screen. A black line occurs when an image line has faded and has not yet been replenished by the next cycle of line production. When I wrote about this effect in Scientific American, I quickly realized that I could not hold the frequency of my humming steady enough to see the black lines. So I pressed a controllable oscillator onto my face and then slowly changed the frequency until the black lines appeared. (Ok, I fully understand just how weird this sounds, and you are right---it really was weird and not something I would do in public.) Professor Matt Anderson of San Diego State University recently described a more tasty method. Crunch down on a large hard pretzel while watching a television screen from a distance. As you crush the pretzel in your mouth, your skull vibrates, briefly oscillating your eyes. If you stand about 20 meters from the tube-type of television or computer monitor, with the screen fully lit up with an image rather than just being blank, you can see brief distortions and black lines across the screen. I cannot see this effect on flat screens but I am not yet convinced that I tried enough pretzels. Let me know what you see if you try this.

7.9 Catching arrowsJearl Walkerwww.flyingcircusofphysics.comDec 2008 Most of the action we see in a modern martial art movie is faked or computer-generated, making the movie little more than an animation film. However, some of the stunts can really be performed by skilled fighters. For example, a person really can catch an arrow in flight, as seen in this video:

You might think that to catch an arrow means that you must follow it with your eyes, from the bow to when it is alongside you in flight. However, the eyes cannot follow such motion, as shown in studies with baseball players. When he stands at the plate with a fastball coming toward him, a major league baseball player can see the ball until it is about 5.5 feet away from the plate, but thereafter the motion is a blur. The problem is that the eyes cannot rotate fast enough for the vision to be fixed on the ball. However, some ball players can track the ball during the first part of its flight and then, anticipating where the ball will cross home plate, jump the vision to that point, in order to see the ball as it is hit with the bat.

An arrow-catcher might do the same vision jump in order to catch the arrow as it passes him. But the arrow-catcher in the video does not use the sight of the arrow at all. Instead, he depends on the sound emitted as the bow as it launches the arrow to trigger his grab into the air. If he moves quickly, the time he takes to clinch his hand matches the time the arrow takes to reach him. As you see in the video, the strategy does not always work. Not only can the timing be off, but the arrow may not be exactly the right place to be grabbed. Of course, this demonstration is highly dangerous for the obvious reason --- the arrow-catcher might end up catching the arrow with his body or head instead of his hand.

7.13 The “rotating snakes” illusion of motionJearl Walker www.flyingcircusofphysics.comJuly 2008 Skilled artists can paint images that range from realistic to impressionistic but the images are always static, even if they suggest motion. At best they are snapshots and not movies. However, there is a certain type of art, dubbed op art for “optical art,” in which most people perceive motion. When I look at certain examples of op art, I sense motion in my peripheral view (off the direct line of sight), as if sections of the art are sneaking around like mice on a kitchen floor. When I turn my gaze toward the moving regions, the motion there stops, as if the mice freeze in place.

The most startling example of op art I have seen is “rotating snakes,” which was created by Professor Akiyoshi Kitaoka of Ritsumeikan University in Japan. It consists of circular arrangements of colored tiles. When I look casually at the art, the circular arrangements in my peripheral view undergo noticeable rotation but when I look directly at any one of those arrangements, the motion immediately disappears, as if the tiles don’t want to be seen while they move. Here’s the link to “rotating snakes,” but let me first warn you that if you are adversely affected by shimmering lights, you probably should not use the link:

Illusions of motion in a static picture fascinate many types of researchers because they provide tantalizing clues as to how not only vision works (which we only poorly understand) but also how the brain works (which we understand even less). The colors of the “rotating snakes” illusion are actually irrelevant. Instead, the important features lie in the contrast in the luminance (loosely said to be the brightness) of adjacent tiles in each circle of tiles. Along each circle the tiles have this repeated arrangement:

black, dark gray, white, light gray, black

The perceived motion is rightward through this arrangement.

No one can explain the illusion in detail but here are some of the main points:

1. When I look at an edge that divides regions with different luminance, the speed of the visual processing needed to bring the image to consciousness depends on both the luminance and the contrast between the two regions. Larger luminance and larger contrast results in faster processing. For the arrangement of tiles, we have

black, dark gray, white, light gray, black

↑ ↑ ↑ ↑

contrast: small large small large

So, the processing of the different tiles occurs at different rates:

black, dark gray, white, light gray, black

↑ ↑ ↑ ↑

contrast: small large small large

↑ ↑

processing: quick delayed

2. When I perceive one edge and then, shortly later, an adjacent edge, the motion sensors in my brain can signal that something moved from the first edge to the second edge. This seems to be the source of the motion illusion.

black, dark gray, white, light gray, black

↑ ↑ ↑ ↑

contrast: small large small large

↑ ↑

processing: quick delayed

perceived motion →

3. If I could stare at the pattern without moving my eyes, not only would I not perceive motion but the pattern itself would probably fade out. The brain quickly ignores constant (unchanging) signals. So, if the pattern remains fixed on my retina, it would soon be ignored.

However, even if I try to fixate my view of the pattern, my eyes still undergo slight motions, drifts and jumps. Part of the normal visual processing is to allow for that motion and bring a steady view up to consciousness. In the “rotating snakes” illusion, the natural drifting of the eyes seems to act as a “screen refresher” because it moves the pattern over the retina, disallowing the brain to fade it out. Because the pattern is continuously being refreshed on the retina, I can then perceive the illusion of motion due to the processing speed of different edges that separate regions with different luminance.

Professor Kitaoka has a wealth of other optical illusions on his web site. After you explore them, you might like to try your hand at creating new designs of op art. There is a lot left in visual science to be explored.

x7.15 Reading in the dark – a weird illusionJearl Walkerwww.flyingcircusofphysics.comSep 2009 Here is another of my examples of “physics for the first date,” and it is also one of the weirdest illusions I have ever experienced. First you and your date need to dark adapt your eyes by waiting in darkness for about 10 to 15 minutes. Place an open magazine in front of you at about normal viewing distance. Of course, in the dark, you cannot see it.

After your eyes have adapted to the dark, illuminate the magazine with a flash of light, such as with a camera or a cell phone with a built-in camera. During the flash, the magazine is too brightly illuminated for your dark-adapted eyes to see any details of it. But hold your gaze steady (don’t move your eyes around). As the glare of the flash fades, a detailed image of the magazine begins to appear. It is said to be a positive afterimage because the white regions on the page appear as white regions in the afterimage and the dark regions (such as words or photographs) appear as dark regions. Moving your eyes will immediately erase the afterimage, but if you hold your gaze steady, you can move your attention over the afterimage to read words and pick out details in any photographs or drawings. This image lasts for about 15 seconds and then is replaced by a negative afterimage, with black and white reversed.

Reading in the dark may be curious but here is the weird part. Trigger the flash twice as, say, a coin falls and then again hold your gaze steady. You will see two afterimages of the coin during the fall, as if they were shot in a stroboscopic photograph. Next, place your hand in front of you, trigger the flash, and then grab the back of your neck with the hand. As the afterimage appears, you clearly see the hand in front you while you clearly feel it on the back of your neck. The sensation is most strange.

Even stranger is this: Look down at the floor, trigger the flash to illuminate the floor, and then (without changing your gaze), squat. When the afterimage appears, you see the floor at its normal distance from your eyes, but from a lifetime of experience you know that from the squatting position it must be much closer. If you flash when squatting and then stand for the afterimage, the floor appears to be cutting through you at about chest level. I sure that you and your date can think of other experiments.

The positive afterimage is the more striking of the two afterimages you see in these demonstrations. Unfortunately there is little known about positive afterimages and no commonly accepted explanation.

The negative afterimage is better understood and is usually attributed to the saturation (bleaching) of the photoreceptors on the retina, especially the cone cells, by bright light or prolonged exposure to light. When light reaches the retina, certain chemical reactions occur which then trigger nerve signals to be sent to visual cortex of the brain. However, over stimulation of the photoreceptors temporarily depletes the chemicals, and those regions of the retina then appear to be darker than the surrounding, undepleted regions, giving the bright-dark reversal that characterizes a negative afterimage. This much is the common explanation of the effect, but experimental evidence indicates that negative afterimages are also due to changes in the processing of the nerve signals in the visual cortex following a bright or prolonged exposure.

7.28 Ornamental ball visual effectJearl Walker www.flyingcircusofphysics.comDecember 2007 Around Christmas time some years ago, Michael Berry, who is famous for a variety of physics insights, including the Berry phase in quantum physics, made a remarkably simple observation about the reflection by a convex curved surface. You can easily repeat that observation. If you examine the image of a small lamp in the side of a shiny ball, such as commonly used to decorate a Christmas tree, the shape of the image depends on the room illumination. When the illumination is normal, the reflection forms a small image that you can clearly identify as that of the lamp. However, if the room lights are dimmed, the image gradually elongates and the final distorted image may not be recognizable.

The distortion involves the way light reflects from the convex surface and how the pupil of your eye changes in response to the general illumination. Light rays from the lamp are reflected in a wide range of directions by the curved surface. When your eye intercepts some of those rays, the only ones that reach the retina and result in a visual sensation are the ones that pass through the pupil, the optical opening to the eye. When the general illumination is relatively bright, the diameter of the pupil is relatively small and so the rays that enter the eye must have about the same angle in their reflection from the ball. The angular spread of those rays is small enough that your visual system can make sense of the rays by mentally extending them back into the ball. What is brought up to consciousness is the image of a small source of light seemingly located behind the surface, much like an image of you is seemingly located behind your bathroom mirror when you look into the mirror.

When you dim the room illumination, your pupil gradually expands to allow in more light, so that you become “dark adapted.” (I usually allow about 10 or 15 minutes for such adaptation.) The now larger pupil allows a larger angular spread of the rays reflected from the curved surface, and the rays can no longer be mentally extended backward to a single point. Instead, they seem to extend back to a line that lies in the plane formed by your eye, the lamp, and the point on the ball closest to your eye. The effect works better if the lamp is tiny, such as a common Christmas tree light or a pinhole pierced into a sheet of aluminum foil that is mounted over the front end of a desk lamp.

If you switch on the room illumination after the line forms, the pupil diameter quickly decreases and the line quickly collapses to a point.

7.33 Pinhole rifle sighting, pinhole glasses, and pinhole selfiesJearl Walkerwww.flyingcircusofphysics.comJuly 2015 With normal vision, a person can clearly see a nearby object and a more distant object, but not simultaneously. To shift from reading a book to seeing a car down the street, I have to adjust the focusing of my eyes, which I do subconsciously by changing the muscle that controls the shape of the lens inside each eye. When I aim a rifle, I need to line up the target (which might be 20 meters down the shooting range) and also the front and rear sights on the rifle, but I cannot see all three things simultaneously --- at least one of them is blurred.

One solution to this common problem is to mount a pinhole device just in front of my shooting eye. By looking through the pinhole I greatly increase the distance through which objects are simultaneously in focus (or nearly in focus). The advantage of the pinhole is that it decreases the angular range of light rays coming from an object and reaching the retina at the rear of the eye.

Suppose I look at a nearby point source of light and a more distant source. If I adjust my eye so that the more distant source is in focus, then light rays from it form a small image on the retina.

However, the light rays from the nearby source then “attempt” to form their image behind the retina.

So, those light rays from the nearby source illuminate a larger region of the retina, and what I see is a fuzzy image of the nearby source.

If I then place a pinhole just in front of my eye, the pinhole allows only part of the light rays from the nearby source to reach the retina. Thus the illuminated range on the retina is smaller and I see a sharper (though dimmer) source.

Pinhole glasses

Pinhole glasses have very dark plastic “lenses” with many pinholes (or tiny clear circles) through which light is transmitted. Suppose a person is far sighted and cannot read a book page. By looking at the page through the pinhole glasses, the letters produce smaller images on the retina and are thus much less fuzzy. This advantage of pinhole glasses has long been known, but unfortunately many false claims have been made about the glasses altering vision in a permanent way so that the person moves toward perfect vision. They do no such thing. For example, this video recommends that you “exercise” the muscles of your eyes for 15 minutes a day by using pinhole glasses. There is no medical evidence that the eyes change.

Pinhole camerasPinhole cameras are still popular even though most designs require photographic film, which is no longer common. Still, they are fun and easy to make, even with a small box. A pinhole is punched in one side of the box, with opaque tape placed over the hole. In a dark room, film is then mounted on the inside wall on the opposite side of the box. The box is kept closed and the pinhole is kept covered until a photograph is to be made. Then the tape is removed. Light from the subject can then enter the box and record an image on the film. Experience is needed to know how long the film is to be exposed, but several minutes are usually required because of the low illumination entering the box.

Recently photographic artist Ignas Kutavicious developed a technique of using a pinhole camera to take a selfie (self image). Here you can see him posing with its equipment.

The drawback is that the person being photographed must remain still for as much as five minutes in order to expose the film sufficiently. Here is a gallery of some of his work:

7.33 Viewing through a pinholeJearl Walkerwww.flyingcircusofphysics.comJuly 2014 As explained very well in this video, you can always improve faulty vision by simply looking through a small opening. For example, if you need glasses or contact lenses, try viewing a street scene without them (well, not if you are driving a car). The scene will be out of focus and thus blurry. Now curl your first finger up along your thumb so that the finger forms a small opening. When you look through that opening at the scene, things will be in focus enough for you to see edges.

The trick works just as well if you are far sighted and need glasses or contact lenses to read. Look through a small opening at the reading material and the words will be readable.

Here comes the video, but here first is the main reasoning. If the world is blurry to you without glasses or contact lenses, the light rays coming from any particular point on an object reaches many points on your retina at the back of your eye. The purpose of glasses or lenses is to bring all those rays to a single point on the retina, to form a single image. If all other points on the object also arrive at individual points instead of being spread out, then you perceive a clear image.

The function of the small opening is to eliminate most of the light rays coming from a point on the object. Only a few rays pass through the opening. They will arrive on your retina with only slight spreading. The image will not as sharp as you would get with corrected vision and will be darker because you have blocked much of the light, but you can still distinguish objects and read.

7.46 Cosmic rays and airplane flightsJearl Walkerwww.flyingcircusofphysics.comJuly 2010 Earth is continuously bombarded by cosmic rays, which are particles that originate either in our Milky Way galaxy or from other galaxies. Most of the particles are protons that are generated by well understood processes, but the generation of the very energetic protons is currently not understood.

As the particles penetrate the higher reaches of the atmosphere, their collisions with air molecules produce secondary particles, including electrons, positrons, and pions. The protons and electrons lose their energy as they continue downward through the atmosphere, and each positron soon combines with an electron along the way --- the pair annihilate each other, producing two gamma rays. The pions quickly decay to produce muons. Muons then decay by transforming into neutrinos and either electrons or positrons. Again, the electrons and positrons quickly lose their energy or undergo annihilation.

Most of the particles reaching sea level are muons. At first glance, they should not be able to travel all the way down to sea level because their average life time is only 2.2 microseconds, as measured when they are stationary. With such a short lifetime, they should decay well before reaching sea level. However, the muons are moving so fast that the relativistic effect known as time dilation applies, and their lifetime as measured in the frame of the ground is much longer than 2.2 microseconds. That longer lifetime allows many of them to reach sea level before they decay.

If you move to greater altitudes by, say, climbing a mountain, the rate of particles reaching you increases. Not only do you intercept more of the muons, but you begin to intercept some of the other particles in the secondary particle shower.

With careful measurements, including proper statistical analysis, you might be able to measure the increase in the particle rate by carrying a Geiger counter along with you as you climb a mountain. In such a device, the passage of a particle (such as a muon), x ray, or gamma ray through the interior causes a cascade of charged particles, which produces a pulse of current in the meter. Collectively, these particles and rays are called ionizing radiation because they can remove electrons from atoms, thus ionizing the atoms. Each pulse generates a signal with an audible click (as you might have heard in movies involving radiation dangers, atomic war, giant insect creatures, and so on). Each pulse also produces a flash of light in a bulb. Thus, the rate of particles passing through the device is indicated by the rate of clicks and flashes.

Mountain climbing with a Geiger counter is actually a difficult way to show that the rate of particles increases with altitude because the rock itself produces ionizing particles and rays due to its radioactive content. Thus, the rate of clicks and flashes does not measure only the particles resulting from cosmic rays.

Recently Francesco Blanco, Paola La Rocca, and Francesco Riggi of the University of Catania and the INFN (both in Catania, Italy) described experiments in which Geiger counters were carried by students on commercial air flights. The count rate was measured as a function of time during the flight, rather than as a function of altitude, because the altitude could not be measured. However, the normal cruising altitude of the flights was known to be between 9 and 10 kilometers. On average, the measured rate at the cruising altitude was about 8 times that at sea level.

The authors point out two complications in interpreting the result in terms of the muon rate. (1) The Geiger counters were somewhat shielded by the airplane body. (2) Although the rate of protons and electrons at sea level was close to zero, their rate at the cruising altitude was about half that of the muons. Still, the experiments admirably demonstrate the increase in muon rate with altitude.

Down below here are links to videos made by other people who happened to carry Geiger counters on airplane trips. Let me explain the units of microsieverts per hour that you see in some of the videos.

The radiation dose (the energy) that, say, you absorb when exposed to radiation is measured in grays (Gy), where 1 gray is the absorption of 1 joule per kilogram in your body. (An older unit of absorbed is the rad, where 1 rad = 0.01 gray.)

However, different types of radiation cause different amounts of damage to your body. So normally we multiply the dose in grays by a number known as the RBE factor, to account for the severity of damage. For example, electrons and muons have an RBE of 1.0, whereas protons have an RBE of 5 to 10 (the value is debated in the research literature). The result of the multiplication is the dose equivalent, measured in units of sieverts (Sv). (An older unit is the rem, where 1 rem = 0.01 sievert.)

What you see in the videos is useful only in a relative sense --- you can see that the count rate at the cruising altitude is significantly higher than that at sea level. However, to interpret the readings in terms of sieverts would require better information about the type of radiation setting off the Geiger counter.

Radiation exposure is of no concern to occasional passengers but not to flight crews who are routinely at high altitudes. If you want to watch a video that I produced about time dilation for the web material associated with my textbook, go to the Facebook site for The Flying Circus of Physics at

and click on “The Relativity of Time.” Using only algebra and Einstein’s own simple explanation, I derive the time dilation equation. You might also watch “The Relativity of Length,” which uses only algebra and the time dilation equation to derive the length contraction equation.

x7.46 Cosmic rays and airplane flightsJearl Walker www.flyingcircusofphysics.comSeptember 2006 Earth's atmosphere partially protects us from energetic particles from the Sun and outer space (cosmic radiation), but that protection is less when you are flying at high altitudes. However, the risk is negligible unless you fly frequently, such as members of aircrews must. Then the exposure to the radiation can be worrisome, especially when the flight is along a polar route (one at high latitudes, near the north pole), such as commonly used for flights between North America and Europe. Such a route is the shortest path between two points such as Toronto and Paris. The trouble is that the charged particles in the influx of radiation are caught by Earth's magnetic field and spiral down into the higher latitudes. Thus a polar route takes the aircrew through a region of incoming radiation. For this reason, a crew might wear radiation badges to monitor their exposure, and an airplane might be equipped with a radiation detector to sound an alarm if the radiation level is unusually high. Such higher radiation is expected if a giant solar flare explodes and shoots a stream of protons into space toward Earth. Usually an aircrew member is limited in the time per year that can be spent flying through the higher latitudes. You might think that the worst radiation risk was on Concorde flights because, when that type of airplane was still flying, its supersonic speed required it to fly much higher than all other (slower) airplanes. In fact, the risk was less on Concorde flights because the flight times were so much shorter.

7.49 Fireworks illusionJearl Walker www.flyingcircusofphysics.comJune 2007 Each year on the night of July 4, many communities in the United States celebrate Independence Day with impressive fireworks that are shot up into the night sky. One common type is a rocket that explodes into countless burning fragments that shoot outward in all directions, moving along paths that remain visible for about a second. The gravitational pull on the fragments curves the paths like it curves the path of a baseball hit to the outfield. If clouds give you a sense of depth to the background sky, the fragments seem to “spill” from the point of the explosion.

However, if the sky is dark, with no sense of depth, you see an illusion in the paths taken by the fragments. Although the ones on the far side of the explosion are truly moving away from you, you perceive them as moving toward you. So, you perceive that all the fragments move toward you, as if someone has fired them from a shotgun aimed in your general direction.

In the Flying Circus book, I offer one published explanation of the illusion: You subconsciously interpret the fragments as moving on the surface of a three-dimensional structure. You have a lifetime of experience of seeing interesting points on a three-dimensional structure, such as lettering on a soup can, and commonly you can see the points only on the near surface, not the (hidden) back surface. So, with the fireworks display, you interpret the fragments as all being on the near side, and that interpretation makes them look as thought they are moving toward you.

Here is another published explanation: If you were to look along railroad tracks, the closer sections occupy a greater angle in your view than the farther sections. Similarly, if an object moves so that the angle it occupies in your view increases, it must be coming closer to you. So it goes with the fireworks fragments. As the spread of the fragments increases in your view, you perceive them as being a composite object that is coming closer to you.

Firework displays can be scary. Surely, the sudden noise and the brilliant light in an otherwise dark sky are momentarily frightening, even to an adult. But part of the fright may also be due to the illusion that each explosion is some invisible agent in the sky shooting burning fragments from a giant weapon at you. Maybe that is why, when I was young, I always hid under the picnic blanket during the machine-gun-like rapid salvo of explosions that marked the end of every fireworks show.

7.51 Vision with mineral eyesJearl Walkerwww.flyingcircusofphysics.comSeptember 2011 The marine mollusk known as chitons are covered with plates made of the mineral aragonite. In the thousands of thin canals that cross these plates there are aesthetes that are photosensitive. On some types of chitons the aesthetes have an ocellus with a lens, which can focus an image on the underlying retina. The surprising feature is that the lens consists of the mineral aragonite and not a protein-water gel that you and most animals have. Normally a tiny mineral would simply scatter light, but in these types of chitons, it is focused. This unusual bit of optics was recently discovered by Daniel I. Speiser, Douglas J. Eenisse, and Sonke Johnsen of Duke University.

Moreover, the researchers found that chiton could focus an image on its retina whether it was in water or in air. That is surprising because the ability of an eye to focus an image depends on the extent of refraction (bending) of light as the light passes into the eye. You probably have noticed this effect when you swim --- your vision changes dramatically when you replace the air next to your eye with water.

To keep tabs on how light refracts when it passes through an interface, we assign different materials different values of an index of refraction. Air has a value that is slightly above the lowest possible value of 1.0. The protein-water gel of your eye is higher. The water in, say, a swimming pool, is almost as high. When your eye is in air, the light must travel from a very low index to a higher index to enter your eye, and there is significant refraction, which is part of the reason images form on your retina. When you are in water, there is little change in the index as light enters your eye, and thus there is significant less focusing.

So, how can a chiton see in both air and water? The aragonite is birefringent, that is, it has two indexes of refraction (1.68 and 1.53), depending on how the light is polarized (how the electric fields of the light oscillate.) The smaller index produces an image behind (deeper than) the one produced by the larger index. When the chiton is in air, the less deep image appears within the lens and the deeper image appears on the retina (and thus is seen). In water, the less deep image appears on the retina (and thus is seen) and the deeper image tends to form behind the eye. Here is my sketch based on a figure in the research paper:

7.52 Pub trick --- converting a small beer into a large beerJearl Walkerwww.flyingcircusofphysics.comNov 2011 We can often be fooled when judging the fluid volume held by a common drinking container, such as a container of beer sold at sporting events. I think the illusion stems from our confusing a container’s volume with its height. That is, we associate a large volume with a tall container, never mind the fact that the diameter of the container also matters. So, if we see two side-by-side containers, one taller than the other, we usually conclude that the taller container holds more volume without considering the diameters. Here is a video that vividly reveals our error:

7.53 Why is the Moon white?Jearl Walkerwww.flyingcircusofphysics.comDecember 2011 Well, the common explanation is that it is illuminated with direct sunlight, which is white to our eyes, meaning that it consists of approximately uniform contributions across the visible spectrum from red to blue (or violet, if you like). Here are some links to photographs of the Moon where you can see the whiteness.

If the Moon is low in the sky, it can be reddish for the same reasons that a low Sun is red: the light must then travel a long distance through the atmosphere to reach your eyes. Along the way it undergoes continuous scattering by air molecules, which weakens the blue end of the spectrum. What finally reaches you is light dominated by the red end of the spectrum.

However, when the Moon is fairly high in the sky, the light passes through less atmosphere, which is not enough to weaken the blue end of the spectrum. Thus, the Moon is white.

Actually I am playing for time here because now I want to show you an image taken on the lunar surface.

The ground is noticeably gray and certainly not white. So the Moon should be gray in our nighttime view of it, not white.

The whiteness is actually an illusion based on our visual system trying to make sense of the luminance and coloration of what we see. In 1929 Adhemar Gelb demonstrated the essence of the illusion, which you can repeat. In an otherwise dark room, arrange for a black disk to be brightly illuminated by a projector. Be sure to illuminate only the disk and not the surroundings. The disk will appear to be white. Next bring a sheet of white paper near the disk so that at least part of it is illuminated. The black disk immediately becomes gray. Take the paper away, and the black disk immediately turns white again.

The Gelb effect demonstrates that your visual system assigns whiteness to the region of highest luminance (the brightest region). The disk is black but in the initial arrangement it is reflecting more light to you than the surrounding darkness of the room. Thus, it appears to be white. When you bring the paper into the light, then the paper becomes the brightest region and it is seen as being white and you then perceive the disk for it is, darker. Thus it goes with the Moon seen against a dark sky. It is brightly lit in sunlight and surrounded by darkness, and so the Moon appears to be white.

More recent research (especially that done by Alan L. Gilchrist at Rutgers University) has demonstrated anchoring of lightness. Two adjacent regions can be compared in terms of brightness and the brighter one will appear to be whiter than the other region. But the degree of white depends on the relative area of the two regions. Let’s assume that the area of the dimmer (less bright) region is somewhat larger than the area of the brighter region and that we can control each area. As we start, the brighter region is whiter due to the Gelb effect.

Now increase the area of the dimmer region. Our interpretation of the color is said to be anchored in that region. As its area increases, it becomes whiter and that causes the brighter region to become even whiter than it was previously. The brighter region can be transformed from a dull white to a brighter white. It can even appear to be so white that we perceived as being self-luminous (like a lamp). This is how the Moon can appear on some nights --- self-luminous.

The Moon also looks white when seen during daylight and thus surrounded by blue sky and possibly white clouds. This illusion is more difficult to explain, but the best explanation that I’ve seen was offered in 2005 by Robert W. Kentridge of University of Durham. Our visual system monitors the various cues in our field of view to make sense of coloration by comparing reflections and interpreting the coloration in the source of light. Of course if we are looking at the Moon, we must also be seeing the surrounding countryside or buildings, all of which are bathed in white sunlight that has been partially filtered by the atmosphere. Our visual system assumes that the Moon is just another part of the scenery and is illuminated by the same source of light. The visual system then colors the Moon white. The explanation is promising but, to me, not fully convincing.

The actual dull grayness of the night-time Moon would certainly have not been as inspiring to poets, artists, and young lovers as the perceived brilliant, sometime self-luminous Moon. So, maybe, just maybe, this visual illusion occurs simply to make the night more beautiful.

7.54 Bees and Van Gogh’s SunflowersJearl Walkerwww.flyingcircusofphysics.comJune 2012 In a 2006 research paper, Lars Chittka (a biologist) and Julian Walker (an installation artist), both of Queen Mary College at the University of London, described a quite curious experiment to see if bees might discriminate between several art works. Two showed flowers: Vincent Van Gogh’s Sunflowers and Paul Gauguin’s A Vase of Flowers. Two did not: Fernand Leger’s Still Life with Beer Mug and Patrick Caulfield’s Pottery. The paintings appear below, in that order.

The researchers used bees that had been raised in a laboratory, feeding on only sugar solutions from feeders. Thus, they had never seen a flower and there was no reason to think that they could identify flowers in a representation. Still, the experiment was interesting.

Copies of the art works were laid out on a floor in a closed room. Once the bees were released in the room, the researchers noted their approach flights and landings. Bees have three color receptors that peak at wavelengths of 350 nanometers (in the ultraviolet), 440 nanometers (in the blue range and called “bee blue”) and 540 nanometers (in the yellow range, although it is called “bee green”). In the wild, the bees would have seen plenty of ultraviolet light from natural flowers. However, from the posters on the floor, there was only a small amount of reflected ultraviolet light from the yellow and white regions. The researchers wondered if the bees would land randomly on the posters or pick special places.

The favorite of the bees was the Van Gogh flowers, in both approaches and landings: 99 of the 146 approach flights were to the flowers, either in the high contrast margin of a flower or the region of contrast around the center of a flower. Seventeen of the approaches were on the signature of “Vincent” that Van Gogh put on the painting using blue on yellow. Of the landings, 13 of the total 15 were on the flowers.

For the Gauguin copy, 25 of the 81 approaches were to the blue flowers (upper right). Two of the landings were on the blue flowers and the other 9 landings were on other flowers.

For the other two paintings, the most popular sites were a large yellow vase, a light blue dish, and a light blue square.

The bees were certainly not recognizing the shape of the flowers in the paintings. Rather, they were responding to colors and color contrasts. They clearly were attracted to the yellow of the Van Gogh flowers, but were also attracted to the high contrast of blue and yellow in the Van Gogh signature. All this was in line with other research on bee vision: From a distance the bees are attracted to yellow regions and then home in on regions with high contrast. Presumably once they are rewarded with nectar in a real flower, they then learn about the shapes of the flowers, but I don’t think that the bees in the experiment could pick out a flower shape from the Van Gogh painting.

7.55 Pub trick --- putting a hole through your handJearl Walkerwww.flyingcircusofphysics.comMay 2013 Look at the palm of your hand. It is, of course, quite solid. Is there some way to give the appearance of a hole through your hand, so that you can see whatever lies on the far side of your hand through the hole?

You can set up such an illusion by tricking your visual system. Normally the system fuses the slightly different views from your two eyes to generate a three-dimensional real world. You take such fusion for granted, but here is a way to use the fusion to generate a nonreal world. Roll up a sheet of paper into a fairly tight tube and then use one eye to look directly ahead and through the tube. Then bring your other hand up next to the tube, palm toward your face. Your visual system will superimpose the cylinder view and the palm view, and you will “see” a hole in your palm through which you can see things on the other side of your palm. The demonstration is given in this video, along with two other optical illusions that depend on visual superposition.

In one of the other illusions, you touch together the tips of your index fingers immediately in front of the bridge of your nose. Then you slowly shift them away from each other and away from your face. As they move, a “sausage” will appear to float in the air between the finger tips, as long you stare straight ahead and do not move your fingers too far from your face. The left side of the sausage is due to the vision from your right eye, and the right side is due to the vision from your left eye. You can identify which is which if you rotate a finger around its length so that the nail of one finger is visible while the nail of the other finger is not.

You can also set up a floating illusion with other objects, but it helps if they are similar. For example, with two one-dollar bills I can float a rectangular strip between them.

In the last illusion, place your right hand so that the knuckle on the thumb is tucked into the bridge of the nose and the palm is perpendicular to your face. Then position the index finger of your left hand near the far side of your right hand, with tip of the finger visible to your right eye and the base of the finger visible to your left eye. The middle section is blocked from either view by your right hand but your visual system still attempts to connect the visible parts. You then see an eerie thin tip of the finger connected to the wider base of the finger.

August 2013 Several years ago Roberto Casati (of the Institut Jean Nicod in Paris) raised a fascinating question: Can you hide your shadow as a young child might try when placing some object over the shadow? We as adults know that is impossible. If you place, say, a sheet of paper over a shadow on the ground, then the shadow is on the paper. It certainly has not disappeared.

Nevertheless, Casati discovered a way to hide a shadow. In following his lead, here are some of my photographs of a pencil supported in bright sunlight by a cardboard tube. The shadows of the tube and pencil lie across paving stones in my driveway. In these first two photos, I see what I would expect: a merger of pencil and tube shadows.

In this next photo, I covered the tube shadow with white sand, taking some care to keep the sand within the shadow. What I now see is pencil shadow then seemingly crosses under the sandy region. The pencil shadow has disappeared in that region, hidden by the sand.

Of course, this is an illusion created by my visual interpretation of the scene. Although the sand is in the shadows of the tube and pencil, it is still bright relative to the dark pencil shadow on either side because the sand grains scatter some of the ambient light from the surroundings to me. My brain no longer interprets the sandy region as being a shadow region. To make sense of the pencil shadow, which I know must be there somewhere, I interpret it as extending under the sand. I believe the illusion weakens if the two ends of the pencil shadow are too far apart.

Here are links to the photos in Casati’s paper in Perception. In one photo you see a similar hiding of a rod shadow by couscous. In the other you see you see a shadow of Casati himself being hidden by a layer of ice in the overlapping shadow of a playground slide. It was taken early in the morning when the Sun had melted away ice from the rest of the playground but not in the shadow of the slide.

Here is another photo I took following a Casati idea in another of his publications. The pencil, which lies across folded cardboard, creates two visually unrelated shadows, one on the cement walkway and one on the cardboard. Here again I have impression that the connection of the shadows on the left and right are hidden, this time by the cardboard.

Of course, if I invert the cardboard, I see the shadow with no illusion: it just runs up and over the cardboard.

7.57 Shadows of moving hairsJearl Walkerwww.flyingcircusofphysics.comDecember 2013 In September an email came into the FCP site from Terry Flannery, who described an optical effect that was brand new to me in spite of decades of my reading through journals devoted to optics and vision:“I happened to be standing with the sun behind me and noticed the shadow of my legs on the floor. I noticed that the shadow of the hairs on my leg seem to appear as I moved my legs (slowly) but as soon as I stopped moving the shadows of the hairs seemed to diffuse and disappear. I'm assuming that this is just an illusion but it certainly appears to be real. Is this effect understood?”

As soon as I read the email, I went outside into the direct sunlight with a hair-filled brush. When I held the brush stationary and close to the concrete driveway, the hair shadows were barely visible. When I then moved the brush horizontally, the hair shadows became distinct black lines.

I can explain the first observation. Because the sun is not a point source of light in our view but instead subtends about half a degree, the edges of any shadow formed in direct sunlight are not sharp. Instead of a distinct edge between bright and dark (called the umbra), there is an intermediate area (the penumbra) with intermediate intensity. That intermediate region is shielded from one side of the Sun but still exposed to the opposite side of the Sun. If the Sun were a point source of light, this region of partial exposure would not occur.

When I position a hair in the sunlight, the shadow is so narrow that the penumbra from one side overlaps the penumbra from the other side. I then see a faint shadow with no distinct dark region. The huge surprise comes when I move the hair: I should then see simply a moving faint shadow but somehow the shadow becomes dark and distinct.

My guess is that I see an overlap of many shadows, each shifted slightly from the previous one. The overlap of many regions of intermediate intensity then gives me a darker shadow that resembles an umbra. However, that is just a guess. Have you got any ideas or references?

7.58 Café wall illusionJearl Walkerwww.flyingcircusofphysics.comFebruary 2015 The café wall illusion is appropriately named because it was first noticed on the exterior wall of a café in Bristol, England.

After I wrote about the illusion in Scientific American, I came face to face with it in the entrance way to the restrooms at the original location of the Exploratorium in San Francisco. (The Exploratorium is filled with such surprises --- I strongly suggest that you visit it many times.)

The illusion is created by a checkered arrangement of black and white tiles that are separated by mortar (grout) with an intermediate brightness. Here is my photograph of the arrangement on the wall at the Exploratorium. Although the mortar lines are strictly horizontal, I see a distinct flaring of the lines left and right. (If you are viewing this photograph on a small screen, the flaring may not be apparent. In that case, check out the video links below.) The flaring and non-horizontal arrangement are illusions.

On the opposite wall of the entrance way I photographed a similar checkered arrangement but here the brightness of the mortar was not intermediate between the tiles; rather it was as bright as the bright tiles. For this wall no illusion of flaring is seen --- the mortar lines are just horizontal in appearance.

The café wall illusion was first studied in 1979 by Richard L. Gregory and Priscilla Heard of the University of Bristol. (A link to their published paper is given in the references below.) They concluded that the illusion of tilt in the “global” checkered arrangement is triggered by an illusion of tilt in “local” (or small) sections of the arrangement. But what exactly causes the local tilt?

In 1986, Bernard Moulden of the University of Reading and M. J. Morgan of University College London suggested the local tilt was caused by the way edges are perceived. The photoreceptors on the retina are grouped into a circular arrangements with a center and a surround. Each circular arrangement is connected to a ganglion cell. If the photoreceptors are unilluminated, their ganglion cell slowly fires signals deeper into the visual system. Under illumination, however, the cells are of two types. The “on-center” type fires signals faster when only its central photoreceptors are illuminated. The “off-center” type fires signals faster when only its surround photoreceptors are illuminated. Both types fire slowly if both the center and the surround are illuminated.

So, the interiors of both the bright white tiles and the dark black tiles result in slow firing and are not very interesting. However, an edge between bright and dark is interesting because on the brighter side an “on-center” cell fires rapidly while on the darker side an “off-center” cell fires rapidly. When the two signals are processed deeper in the visual system, you perceive the edge.

Let’s look at the café wall pattern where you get rapidly-fired signals from the edges and mortar rather than the tile interiors. Where two white tiles are separated by the mortar, the relatively dark mortar cause off-center cells to rapidly send signals. That perceived mortar line then blends into the edges of the adjacent dark tiles, and the result is a perceived tilt.

Where two dark tiles are separated by the mortar, the relatively bright mortar causes on-center cells to rapidly send signals. That line of mortar blends into the adjacent bright tiles, and, again, the result is a perceived tilt. Thus, the perceived tilt in a small section of the display can trigger a perception of tilt for the entire display.

This explanation of the illusion is promising but may not be complete. Indeed, researchers continue to study the café wall illusion and other tilt illusions.

At the top in the display you can play a video that explains how to use the array just below the video. In the array you can alter the tile spacing and the width and brightness of the grout (mortar), to make the café wall illusion come and go.

This question was addressed by H. W. Leibowitz in a 1985 paper in the American Scientist. Part of the problem is the basic safety design at the crossing. The warnings must begin such that a collision can be avoided for the fastest train, the slowest car, and the worst weather. That means that a motorist who obeys the warning and stops might be waiting a long time when a slow train is actually coming. With experience of long delays before trains even show up, a motorist might choose to drive over the crossing. Of course, getting away with that a few times can lead to a habit of ignoring the warnings.

This might explain the behavior of a motorist near the crossing but how about those more distant motorists who can see the train approaching the crossing and then attempt to beat the train there. Leibowitz argued that the size of the train creates an illusion about the train’s speed. After years of driving, motorists can estimate the speed of another car approaching an intersection along a perpendicular road. But a train is much larger than a car. That larger size results in a perceived slower speed, thus giving the possible illusion that the motorist might beat the train to the crossing. Leibowitz suggested how we might see this speed illusion in a more common setting: When you are at an airport and can watch airplanes land, note that the very large airplanes appear to land at noticeably slower speeds than smaller airplanes. However, the landing speeds are actually all about the same.